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class SignalCorrelation {
/** Approximate {@code sin(i / 1000)}. */
public static double sin(int i) {
double x = i / 1000.0;
double term3 = (x*x*x) / (3 * 2 * 1);
double term5 = (x*x*x*x*x) / (5 * 4 * 3 * 2 * 1);
return x - term3 + term5;
}
public static double[] sinTable(int n) {
double[] table = new double[n];
for (int i = 0; i < n; i++) {
table[i] = sin(i);
}
return table;
}
/** Approximate {@code cos(i / 1000)}. */
public static double cos(int i) {
double x = i / 1000.0;
double term2 = (x*x) / (2 * 1);
double term4 = (x*x*x*x) / (4 * 3 * 2 * 1);
return 1 - term2 + term4;
}
public static double[] cosTable(int n) {
double[] table = new double[n];
for (int i = 0; i < n; i++) {
table[i] = cos(i);
}
return table;
}
public static double correlate(double[] a, double[] b) {
double correlation = 0.0;
for (int i = 0; i < a.length; i++) {
correlation += a[i] * b[i];
}
return correlation;
}
public static double computeCorrelation(double[] a, double[] b) {
return correlate(a, b);
}
public static void main(String[] args) {
int n = args.length > 0 ? Integer.valueOf(args[0]) : 100_000_000;
for (int j = 0; j < 10; j++) {
long tablesStart = System.nanoTime();
double[] sin = sinTable(n);
double[] cos = cosTable(n);
long tablesEnd = System.nanoTime();
System.out.println("table computation: " + (tablesEnd - tablesStart) / 1_000_000 + " ms");
long correlationStart = System.nanoTime();
double sinSin = computeCorrelation(sin, sin);
double sinCos = computeCorrelation(sin, cos);
double cosSin = computeCorrelation(cos, sin);
double cosCos = computeCorrelation(cos, cos);
double sinSinNormalized = sinSin / sinSin;
double sinCosNormalized = sinCos / Math.sqrt(sinSin * cosCos);
double cosSinNormalized = cosSin / Math.sqrt(cosCos * sinSin);
double cosCosNormalized = cosCos / cosCos;
long correlationEnd = System.nanoTime();
System.out.println("sin/sin correlation: " + sinSinNormalized);
System.out.println("sin/cos correlation: " + sinCosNormalized);
System.out.println("cos/sin correlation: " + cosSinNormalized);
System.out.println("cos/cos correlation: " + cosCosNormalized);
System.out.println("correlation: " + (correlationEnd - correlationStart) / 1_000_000 + " ms");
}
}
}
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